Understanding Generalized Advantage Estimate in reinforcement learning
Bootstrapped estimate is biased because it based on $V(s_{t+1})$ which is usually a biased estimate by some estimator such as neural network.

I don't think this statement is totally correct in the context of the paper. Quoting the paper:

Taking $\gamma &lt; 1$ introduces bias into the policy gradient estimate, regardless of the value function’s accuracy. On the other hand, $ \lambda &lt; 1$ introduces bias only when the value function is inaccurate.

So the initial $\gamma$-discounting introduces bias regardless of the accuracy of the $V(s)$.
Same point is reiterated in the footnote on the page 3:

Note, that we have already introduced bias by using $A^{\pi,\gamma}$ in place of $A^\pi$; here we are concerned with obtaining an unbiased estimate of $g^\gamma$, which is a biased estimate of the policy gradient of the undiscounted MDP.

To summarize the above:

the original MDP under consideration is undiscounted
authors introduce $\gamma$-discounting to reduce variance (at cost of bias) of the PG estimate - this happens even if we had accurate $V(s)$
later, authors introduce another $\lambda$-discounting which also controls bias-variance tradeoff - now due to inaccuracy in $V(s)$

As for why lower $\gamma$ reduces variance (p.2 above) - your explanation is on point: smaller $\gamma$ $\Rightarrow$ smaller weights for distant rewards $\Rightarrow$ less variance (but more bias).